Are you sure about the first rule? It doesn't seem necessary according to https://oeis.org/A014575.
The problem is really fun.
cheating
Since I created the problem series and want the Functions I badge, I thought I'd provide the solution that incorporates vampire_factor and are_fangs. Not a great score, but readable!
Sorry, I mean the Magic Numbers badge.
Like it
3986 Solvers
Longest run of consecutive numbers
1801 Solvers
423 Solvers
Relative ratio of "1" in binary number
410 Solvers
Find my daddy long leg (No 's')
660 Solvers
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